Appendix B: Principles Of Operation - Prior Scientific ProScan III Manual

ProScan® III Manual
Appendix B – Principles of operation
Repeatability and Accuracy are important considerations when evaluating stage
performance. Metric Accuracy is simply defined as the difference between the requested
and the actual motion performed by a linear motion device. Repeatability is defined as the
ability of a device to reproduce to a given position. Resolution is then defined as the
smallest movement or step size the device is capable of. Note: The resolution of the X
and Y axes are usually different from that of the Z axis or focus resolution. The Marksman
Analogy shown below attempts to pictorially demonstrate the difference between metric
accuracy and repeatability. The target on the left shows a cluster of shots that are all in
the same basic location, yet not in the desired location (the centre of the target). The
marksman was repeatable, but not accurate. The target on the right has all of the shots
close together and at the centre of the target. The marksman that took these shots is
both accurate and repeatable. Some motorized stage manufacturers overstate their stage
accuracy by using the Root Mean Square (RMS) definition of accuracy.
Prior Scientific uses the Standard Deviation Method. When Prior Scientific quotes stage
accuracy, 3 sigma accuracy (+/- 3 Standard Deviations) is used. This means that 99.74% of
all movements made by our stage will be within our stated accuracy or repeatability range.
The following example compares RMS and 3 Sigma Accuracy. Consider a stage at the
'Home' position which is 1 micron in the X axis away from the stage zero position. The
stage can be cycled through a series of moves which take the stage away from 'Home' and
then return to 'Home' at which point the actual position in the X axis is measured. After
14 cycles, the following data may be collected; 1.8, 1.5, 0.1, 1.7, 1.8, 1.1, 1.8, 0.9, 1.8, 2.0,
0.0, 1.5, 0.9, 1.8. The 3 sigma accuracy for these moves is +/-1.0 microns, while the RMS
accuracy is +\-0.7 microns! The stage can be shown mathematically to have 2 different
accuracies. However, the data shows that 1/2 of the measured values fall outside the 0.7
RMS accuracy range, while all the data fall within the 3 Sigma accuracy range. Calculating
accuracy using the RMS method exaggerates the accuracy of a stage.
© Prior Scientific Instruments Ltd Version 1.12 June 2017 Page 80